Arginine vasopressin (AVP) plays a major role in the homeostasis of fluid balance, vascular tonus, and the regulation of the endocrine stress response. The measurement of AVP levels is difficult due to its short half-life and laborious method of detection. Copeptin is a more stable peptide derived from the same precursor molecule, is released in an equimolar ratio to AVP, and has a very similar response to osmotic, hemodynamic, and stress-related stimuli. In fact, copeptin has been propagated as surrogate marker to indirectly determine circulating AVP concentrations in various conditions. Here, we present an overview of the current knowledge on AVP and copeptin in perinatology with a particular focus on the baby's transition from placenta to lung breathing. We performed a systematic review of the literature on fetal stress hormone levels, including norepinephrine, cortisol, AVP, and copeptin, in regard to birth stress. Finally, diagnostic and therapeutic options for copeptin measurement and AVP functions are discussed.